September 11, 2017
TITLE: New asymptotically conical G2-manifolds

ABSTRACT: Until now, the only examples of asymptotically conical -manifolds that have been proved to exist are the three cohomogenity one examples of Bryant and Salamon. I will discuss cohomogeneity one examples on the total spaces of complex line bundles over S2 x S3, whose asymptotic links are quotients of the standard nearly Kähler S3 x S3.

June 5, 2017
TITLE: Twisted connected sum G2-manifolds

June 6, 2017
TITLE: Topological invariants of G2-manifolds

September 6, 2016
TITLE: Complete and conically singular G2-manifolds of cohomogeneity one

ABSTRACT: Bryant and Salmon’s cohomogeneity 1 examples of complete, asymptotically conical -manifolds provide a model for desingularising compact -manifolds with conical singularities; however no examples of the latter are yet known, and there are also no further known examples of asymptotically conical -manifolds. Theoretical physicists such as Cvetic-Gibbons-Lu-Pope and Brandhuber-Gomis-Gubser-Gukov have considered complete cohomogeneity 1 -manifolds that are “asymptotically locally conical”–the model at infinity is a circle bundle over a cone–and which in a 1-parameter family converge to an asymptotically conical manifold. However, only some of these families have been studied rigorously (Bazaikin-Bogoyavlenskaya).

I will discuss joint work in progress with Foscolo and Haskins on these families, and some of their limits, which include a new asymptotically conical -manifold and a conically singular -manifold with locally conical asymptotics. The latter may provide an avenue to construction of compact -manifolds with conical singularities.